On the integral kernels of derivatives of the Ornstein–Uhlenbeck semigroup

None, None

On the integral kernels of derivatives of the Ornstein–Uhlenbeck semigroup

Journal Article (2016)

Author(s)

Jonas Teuwen (TU Delft - Analysis)

Hermite polynomials Ornstein–Uhlenbeck Mehler kernel Gaussian measure Caldéron reproducing formula

DOI related publication

https://doi.org/10.1142/S0219025716500302 Final published version

To reference this document use

https://resolver.tudelft.nl/uuid:e5aa1e87-f57d-4ce2-bbc1-54a8e6c96eb8

More Info

expand_more

Publication Year

2016

Language

English

Journal title

Infinite Dimensional Analysis, Quantum Probability and Related Topics

Issue number

4

Volume number

19

Article number

1650030

Pages (from-to)

1-13

Downloads counter

202

Abstract

This paper presents a closed-form expression for the integral kernels associated with the derivatives of the Ornstein–Uhlenbeck semigroup e tL etL. Our approach is to expand the Mehler kernel into Hermite polynomials and apply the powers L N LN of the Ornstein–Uhlenbeck operator to it, where we exploit the fact that the Hermite polynomials are eigenfunctions for L L. As an application we give an alternative proof of the kernel estimates by Ref. 10, making all relevant quantities explicit.